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ChainRules.jl
forward and reverse mode automatic differentiation primitives for Julia Base + StdLibs
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The Julia ecosystem provides has a library that includes the differentiation rules hinted at at the end.
https://github.com/JuliaDiff/ChainRules.jl is used by (almost all) automatic differentiation engines and provides an extensive list of such rules.
If the example used sin|cos the auto diff implementations in Julia would have called native cos|-sin and not encurred such a "truncation error". However the post illustrates the idea in a good way.
Good post oxinabox